Hi all.
I am frequently asked how to bush a steel rod (the rod) to ensure that all tape bushings "grip" the inside of the blank to shape a grip.
Lets consider a rod with 3 tape bushings.
We will assume that the wall thickness and taper is consistent.

1. Wrap tape on the forward most tip of the steel rod such that it comes-up tight in the blank with about 3"-4" of the rod extending outside the blank. You may have to remove some tape to get it correct. Make a mark on the rod where it exits the end of the blank.
2. Remove the rod and lay it next to the blank with the mark you made at the end of the blank.
3. Mark the blank and rod where the 2nd and 3rd tape bushings will be.
4. Using a micrometer measure (to 3 places) the O.D. of both the first tape bushing and the first mark on the blank.
5. use the following formula where "A" is the O.D. of the first tape bushing and "B" is the O.D. of the blank opposite the first bushing and "C" is the O.D. of the blank at the location of the 2nd tape bushing - and "X" is the diameter of what the 2nd tape bushing will be.

"A" is to "B" as "X" is to "C"

"A" over "B" = "X" over "C"

"B" times "X" = "A" times "C"

Divide both sides by "B"

"X" = the OD of the second bushing.
Repeat for the third bushing.

Herb

Here all this time I've been measuring the diameter of the reamer or drill at the points that the bushings would go and using that for the taped bushings on the mandrel. I could have used this system instead, to each there own I guess.

Herb,
Your method works very well.

However, this is the method that I use.

I put wraps on the mandrel and insert it into the location that needs to be filled. I put the wrapper part of the rod to the smallest part of the item that I am wanting to fill. I check to see if there is any movement vertically in the bushing. If the bushing won't fit because it is too larger, I take it out and strip off a few wraps. I continue until the bushing is a nice fit.
Then, I go onto the next largest bushing adding just a few more wraps than the previous one. Repeat.
Go on with the procedure until all of the bushings are complete.

I keep a caliper handy to use as a reference tool, once I have determined the first arbor to fit. Then, I use the caliper to slightly increase the size of the bushing as needed for the other part of the setup.

Same principle, but with just a few modifications and no need to do any math, unless you want to do some math.

Good luck